This is an implicitly defined curve. You are told that the solution should look like
this must hold for all y and t
You have so the implict solution is
we can check this by taking the derivative
Question: Solve the Initial value problem:
Express your answer in the form , where has no constant term.
Attempt at the question:
First of all I checked the terms to see if they were exact and they are not. I took the integral with respect to for which is the first part of the equation and it came out to be . Afterwards I took the partial with respect to y of that integral we just got which was: . I now would equate both these equations together and would cancel terms. The result gives me . So, my equation . But my question now is, how do I solve using the initial values since my equation has both terms and ?
Thanks for everyone who contributes!